The following are musical notes in “increasing order”:
The difference between consecutive notes is a semitone, and the sequence wraps around so the note that is one semitone above $G\sharp $ is $A$. The difference between a tone is the same as two semitones. So the note that is one tone above $B$ is $C\sharp $. The note that is one tone above $G$ is $A$.
We do not worry about flats such as $C\flat $ nor do we worry about adding a $\sharp $ sign to $B$ and $E$ in this problem (they are aliases for notes that are already listed).
A major scale is defined by a note (such as $A$ or $C\sharp $) and all other notes following that one in an arithmetic progression:
The starting note appears in the name of the scale.
For example, the scale $A\sharp $-major consists of the following notes:
(by convention, the first note is repeated at the end of the sequence).
Note that $A\sharp $-major is typically not considered a standard musical scale. It is identical in sound to $B\flat $, and proper notation of $A\sharp $-major would require the use of double-sharps. We ignore such issues in this problem and just use the $12$ notes given at the top of this problem.
Finally, in this problem a song is just a sequence of notes. Your job is to identify all major scales such that the song uses only notes in that scale.
The first line of input is an integer $1\leq n \leq 100$ denoting the number of notes played in a song. The second line consists of a sequence of notes, separated by spaces.
Output consists of a single line that lists all scales the song may be played in. Consecutive scales should be separated by a single space and the scales must appear in lexicographic order. If the song may not fit in any one of these scales, simply output a line containing the text none.
|Sample Input 1||Sample Output 1|
10 C D F D C D F F F C
A# C D# F
|Sample Input 2||Sample Output 2|
6 A B A F# G# C